申論題

3. A couple argues over what to do over the weekend. There are two options: a football game and shopping. They both want to spend the weekend together, but they cannot agree over what to do. The wife likes shopping much better than football, but the husband likes football better than shopping. Since the couple wants to spend time together, if they go separate ways, they will receive no utility and the payoff will be “0”. If they go either shopping or watching a football game, both will receive some utility form the fact that they’re together. If they go shopping, the payoff to the wife, who really enjoys the activity, is then “3”, and the payoff to the husband is “1”. If they go watching a football game, the payoff to the wife is then “1”, and the payoff to the husband, who really enjoys the activity, is “3”. Use the above information to answer the following questions.

(c). If the game is sequential move and the wife moves first, what will be the sub-game perfect Nash equilibrium? Explain.